Problem: Simplify the following expression: $k = \dfrac{15q + 5}{30p + 5r} + \dfrac{5p}{30p + 5r}$ You can assume $p,q,r \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{15q + 5 + 5p}{30p + 5r}$ The numerator and denominator have a common factor of $5$, so we can simplify $k = \dfrac{3q + 1 + p}{6p + r}$